The process of elimination based on facts and physical measurements, not "I think..." is the best way to perform troubleshooting. Ockham's Razor would indicate that after verifying battery voltage and capacity the next thing would be wiring connections. After that the wiring itself. Lastly, the devices connected to the wiring.
Considering that the problem arose when the level of vibration was at or near its highest, and the battery was shown to have good voltage, one can pretty safely conclude a connection/wiring problem.
If only the battery is replaced and nothing else touched, I bet it will crash again.
Good Luck.